Answers to Textbook Questions and Problems CHAPTER 14 Aggregate Supply and the Short-Run Tradeoff Between Inflation and Unemployment Questions for Review 1. In this chapter, we looked at two models of the short-run aggregate supply curve. Both models attempt to explain why, in the short run, output might deviate from its long-run “natural rate”—the level of output that is consistent with the full employment of labor and capital. Both models result in an aggregate supply function in which output deviates from its natural rate Y when the price level deviates from the expected price level: Y = Y + α(P – EP). The first model is the sticky-price model. The market imperfection in this model is that prices in the goods market do not adjust immediately to changes in demand conditions—the goods market does not clear instantaneously. If the demand for a firm’s goods falls, some respond by reducing output, not prices. The second model is the imperfect-information model. This model assumes that there is imperfect information about prices, in that some suppliers of goods confuse changes in the price level with changes in relative prices. If a producer observes the nominal price of the firm’s good rising, the producer attributes some of the rise to an increase in relative price, even if it is purely a general price increase. As a result, the producer increases production. In both models, there is a discrepancy between what is really happening and what firms think is happening. In the sticky-price model, some firms expect prices to be at one level and they end up at another level. In the imperfect-information model, some firms expect the relative price of their output has changed when it really has not. 2. In this chapter, we argued that in the short run the supply of output depends on the natural rate of output and on the difference between the price level and the expected price level. This relationship is expressed in the aggregate-supply equation: Y = Y + α(P – EP). The Phillips curve is an alternative way to express aggregate supply. It provides a simple way to express the tradeoff between inflation and unemployment implied by the short-run aggregate supply curve. The Phillips curve posits that inflation π depends on the expected inflation rate Eπ, on cyclical unemployment u – un, and on supply shocks v: π = Eπ – β(u – un) + v. Both equations tell us the same information in a different way: both imply a connection between real economic activity and unexpected changes in prices. In addition, both the Phillips curve and the short-run aggregate supply curve show that inflation and unemployment move in opposite directions. 3. Inflation is inertial because of the way people form expectations. It is plausible to assume that people’s expectations of inflation depend on recently observed inflation. These expectations then influence the wages and prices that people set. For example, if prices have been rising quickly, people will expect them to continue to rise quickly. These expectations will be built into the contracts people set, so that actual wages and prices will rise quickly. In addition, both the Phillips curve and the short-run aggregate supply curve show that inflation and unemployment move in opposite directions. 4. Demand-pull inflation results from high aggregate demand: the increase in demand “pulls” prices and output up. Cost-push inflation comes from adverse supply shocks that push up the cost of production— for example, the increases in oil prices in the mid- and late-1970s. The Phillips curve tells us that inflation depends on expected inflation, the difference between unemployment and its natural rate, and a shock v: π = Eπ – β(u – un) + v. The term “ – β(u – un)” is the demand-pull inflation, since if unemployment is below its natural rate (u EP, output rises. But it is only the unanticipated part of money growth that increases output. b. The Fed often tries to stabilize the economy by offsetting shocks to output and unemployment. For example, it might increase the money supply during recessions in an attempt to stimulate the economy, and it might reduce the money supply during booms in an attempt to slow it down. The Fed can only do this by surprising people about the price level: during a recession, they want prices to be higher than expected, and during booms, they want prices to be lower than expected. If people have rational expectations, however, they will expect the Fed to respond this way. So if the economy is in a boom, people expect the Fed to reduce the money supply; in a recession, people expect the Fed to increase the money supply. In either case, it is impossible for the Fed to cause (P – EP) to vary systematically from zero. Since people take into account the systematic, anticipated movements in money, the effect on output of systematic, active policy is exactly the same as a policy of keeping the money supply constant, assuming the Fed chooses the level of the money supply at the same time people set prices so everyone has the same information. c. If the Fed sets the money supply after people set wages and prices, then the Fed can use monetary policy systematically to stabilize output. The assumption of rational expectations means that people use all of the information available to them in forming expectations about the price level. This includes information about the state of the economy and information about how the Fed will respond to this state. This does not mean that people know what the state of the economy will be, nor do they know exactly how the Fed will act: they simply make their best guess. As time passes, the Fed learns information about the economy that was unknown to those setting wages and prices. At this point, since contracts have already set these wages and prices, people are stuck with their expectations EP. The Fed can then use monetary policy to affect the actual price level P, and hence can affect output systematically. 7. In this model, the natural rate of unemployment is an average of the unemployment rates in the past two years. Hence, if a recession raises the unemployment rate in some year, then the natural rate of unemployment rises as well. This means that the model exhibits hysteresis: short-term cyclical unemployment affects the long-term natural rate of unemployment. a. The natural rate of unemployment might depend on recent unemployment for at least two reasons, suggested by the theory of hysteresis. First, recent unemployment rates might affect the level of frictional unemployment. Unemployed workers lose job skills and find it harder to get jobs; also, unemployed workers might lose some of their desire to work, and hence search less hard for a job. Second, recent unemployment rates might affect the level of structural unemployment. If labor negotiations give a greater voice to “insiders” than “outsiders,” then the insiders might push for high wages at the expense of jobs. This will be especially true in industries in which negotiations take place between firms and unions. b. If the Fed seeks to reduce inflation permanently by 1 percentage point, then the Phillips curve tells us that in the first period we require π1 – π0 = –1 = –0.5(u1 – un1), or (u1 – un1) = 2. That is, we require an unemployment rate 2 percentage points above the original natural rate u. Next period, however, the natural rate will rise as a result of the cyclical unemployment. The new natural rate u will be u = 0.5[u1 + u0] = 0.5[(un1 + 2) + un1] = un1 + 1. Hence, the natural rate of unemployment rises by 1 percentage point. If the Fed wants to keep inflation at its new level, then unemployment in period 2 must equal the new natural rate u. Hence, u2 = un1 + 1. In every subsequent period, it remains true that the unemployment rate must equal the natural rate. This natural rate never returns to its original level: we can show this by deriving the sequence of unemployment rates: u3 = (1/2)u2 + (1/2)u1 = u + 1.5 u4 = (1/2)u3 + (1/2)u2 = u + 1.25 u5 = (1/2)u4 + (1/2)u3 = u + 1.375. Unemployment always remains above its original natural rate. In fact, we can show that it is always at least 1 percent above its original natural rate. Thus, to reduce inflation by 1 percentage point, unemployment rises above its original level by 2 percentage points in the first year, and by 1 or more percentage points in every year after that. c. Because unemployment is always higher than it started, output is always lower than it would have been. Hence, the sacrifice ratio is infinite. d. Without hysteresis, we found that there was a short-run tradeoff but no long-run tradeoff between inflation and unemployment. With hysteresis, we find that there is a long-run tradeoff between inflation and unemployment: to reduce inflation, unemployment must rise permanently. 8. a. The natural level of output is determined by the production function, Y=F(K,L) . If a tax cut raises work effort, it increases L and, thus, increases the natural rate of output. b. The tax cut shifts the aggregate demand curve outward for the normal reason that disposable income and, hence, consumption rise. It shifts the long-run aggregate supply curve outward because the natural rate of output rises. The effect of the tax cut on the short-run aggregate supply (SRAS) curve depends on which model you use. The labor supply curve shifts outward because workers are willing to supply more labor at any given real wage while the labor demand curve is unchanged. In the sticky-price model the quantity of labor is demand-determined, so the SRAS curve does not move. By contrast, the imperfect-information model assumes that the labor market is always in equilibrium, so the greater supply of labor leads to higher employment immediately: the SRAS shifts out. c. If you are using the sticky-price model, the short-run analysis is the same as the conventional model without the labor-supply effect. That is, output and prices both rise because aggregate demand rises while short-run aggregate supply is unchanged. If you use the imperfect-information model, short-run aggregate supply shifts outward, so that the tax cut is more expansionary and less inflationary than the conventional model. Figure 14-5 shows the effects in both models. Point A is the original equilibrium, point SW is the new equilibrium in the sticky-price model, and point II is the new equilibrium in the imperfect-information model. d. In the normal model, where the tax cut does not lead to a shift of labor supply that increases the natural level of output, the long-run price level will be higher as a result of the tax cut and output will return to the same natural level. The tax cut led to a rightward shift of the aggregate demand curve in the short run. In the long run, the short-run aggregate supply curve will shift up and to the left as the expected price level rises. In the alternative model, where the tax cut leads to an increase in the natural level of output, the long-run results depend on whether the horizontal shift in the aggregate demand curve is larger, smaller, or the same as the horizontal shift in the long-run aggregate supply curve. If the two shift horizontally by the same amount, then the price level is unaffected in the long run. If the shift in aggregate demand is greater than the shift in the long-run aggregate supply curve, then the price level will be higher in the long run. 9. From the BLS Web site (www.bls.gov), there are various ways to get the CPI data. For the years 2009– 2014, I obtained the following for “all urban consumers”: CPI inflation CPI rate, excluding excluding CPI inflation food and food and Year CPI rate energy energy 2009 214.537 219.235 2010 218.056 1.64% 221.337 0.96% 2011 224.939 3.16% 225.008 1.66% 2012 229.594 2.07% 229.755 2.11% 2013 232.957 1.46% 233.806 1.76% 2014 236.736 1.62% 237.897 1.75% The overall CPI was clearly more volatile than the CPI excluding food and energy. The difference reflects shocks to the price of food and energy—especially energy prices, which are highly variable. When energy prices go down, the total CPI will rise less than the CPI excluding food and energy. This represents a supply shock, which shifts the aggregate supply curve and Phillips curve downward. More Problems and Applications to Chapter 14 1. a. The classical large open economy model (from the appendix to Chapter 6) is similar to special case 2 in the text, except that it allows the interest rate to deviate from the world interest rate. That is, this is the special case where EP = P, L(i, Y) = (1/V)Y, and CF = CF(r–r*), with a non-infinitely elastic international capital flow. Because capital flows do not respond overwhelmingly to any differences between the domestic and world interest rates, these rates can, in fact, vary in this case. b. The Keynesian cross model of Chapter 11 is the special case where (i) the economy is closed, so that CF(r–r*) = 0; (ii) I(r) = I, so that investment is given exogenously; and (iii) α is infinite, so that the short-run aggregate-supply curve is horizontal. In this special case, output depends solely on the demand for goods and services. c. The IS–LM model for the large open economy (from the appendix to Chapter 13) is the special case where α is infinite and CF = CF(r–r*) is not infinitely elastic. In this case, the short-run aggregate supply curve is horizontal, and capital flows do not respond too much to differences between the domestic and world interest rates. IN THIS CHAPTER, YOU WILL LEARN: ▪two models of aggregate supply in which output depends positively on the price level in the short run ▪about the short-run tradeoff between inflation and unemployment known as the Phillips curve Introduction ▪ In previous chapters, we assumed the price level P was “stuck” in the short run. ▪ This implies a horizontal SRAS curve. ▪ Now, we consider two prominent models of aggregate supply in the short run: ▪ Sticky-price model ▪ Imperfect-information model Introduction ▪Both models imply: Y Y= +(P EP− ) agg. expected output price level a positive natural rate parameter actual of output price level ▪ Other things equal, Y and P are positively related, so the SRAS curve is upward sloping. ▪ Reasons for sticky prices: ▪ long-term contracts between firms and customers ▪ menu costs ▪ firms not wishing to annoy customers with frequent price changes ▪ Assumption: ▪ Firms set their own prices (e.g., as in monopolistic competition). ▪ An individual firm’s desired price is: p = +P a Y Y( − ) where a > 0. Suppose two types of firms: • firms with flexible prices, set prices as above • firms with sticky prices, must set their price before they know how P and Y will turn out: p = EP a EY EY+ ( − ) p = EP a EY EY+ ( − ) ▪ Assume sticky-price firms expect that output will equal its natural rate. Then, p = EP ▪ To derive the aggregate supply curve, first find an expression for the overall price level. ▪ s = fraction of firms with sticky prices. Then, we can write the overall price level as… P = s EP[ ] (+ −1 s P a Y Y)[ + ( − )] price set by price set by sticky-price firms flexible-price firms ▪ Subtract (1−s)P from both sides: sP = s EP[ ] (+ −1 s a Y Y)[ ( − )] ▪ Divide both sides by s: P = EP + (1−s a) (Y Y− ) s P = EP + (1−s a) (Y Y− ) s ▪ High EP High P If firms expect high prices, then firms that must set prices in advance will set them high. Other firms respond by setting high prices. ▪ High Y High P When income is high, the demand for goods is high. Firms with flexible prices set high prices. The greater the fraction of flexible-price firms, the smaller is s and the bigger the effect of Y on P. P = EP + (1−s a) (Y Y− ) s ▪ Finally, derive AS equation by solving for Y : Y Y= +(P EP− ), s where = 0 (1−s a) The imperfect-information model Assumptions: ▪ All wages and prices are perfectly flexible, all markets are clear. ▪ Each supplier produces one good, consumes many goods. ▪ Each supplier knows the nominal price of the good she produces, but does not know the overall price level. The imperfect-information model ▪ Supply of each good depends on its relative price: the nominal price of the good divided by the overall price level. ▪ Supplier does not know price level at the time she makes her production decision, so uses EP. ▪ Suppose P rises but EP does not. ▪ Supplier thinks her relative price has risen, so she produces more. ▪ With many producers thinking this way, Y will rise whenever P rises above EP. Summary & implications P LRAS Y curve & equation. Summary & implications SRAS equation: Y Y= +(P EP− ) Suppose a positive AD shock moves output above its natural rate and P above the level people had expected. Over time, EP EP rises, 2 SRAS shifts up, Y3 =Y Y1 = Inflation, unemployment, and the Phillips curve The Phillips curve states that π depends on ▪ expected inflation, Eπ ▪ cyclical unemployment: the deviation of the actual rate of unemployment from the natural rate ▪supply shocks, (Greek letter “nu”). = E − (u u− n) + where β > 0 is an exogenous constant. Deriving the Phillips curve from SRAS (1) Y Y= +(P EP− ) (2) P EP= + (1)(Y Y− ) (3) P EP= + (1)(Y Y− +) (4) (P P− −1) = (EP P− −1) + (1)(Y Y− +) (5) = E + (1)(Y Y− +) (6) (1)(Y Y− =−) (u u− n) (7) = E − (u u− n) + Comparing SRAS and the Phillips curve SRAS: Y Y= +(P EP− ) Phillips curve: = E − (u u− n)+ ▪ SRAS curve: Output is related to unexpected movements in the price level. ▪ Phillips curve: Unemployment is related to unexpected movements in the inflation rate. Adaptive expectations ▪ Adaptive expectations: an approach that assumes people form their expectations of future inflation based on recently observed inflation. ▪ A simple version: Expected inflation = last year’s actual inflation E = −1 ▪ Then, Phillips curve eq’n becomes = −1 − (u u− n) + Inflation inertia = −1 − (u u− n) + In this form, the Phillips curve implies that inflation has inertia: ▪ In the absence of supply shocks or cyclical unemployment, inflation will continue indefinitely at its current rate. ▪ Past inflation influences expectations of current inflation, which in turn influences the wages & prices that people set. Two causes of rising & falling inflation = −1 − (u u− n) + ▪ cost-push inflation: inflation resulting from supply shocks Adverse supply shocks typically raise production costs and induce firms to raise prices, pushing inflation up. ▪demand-pull inflation: inflation resulting from demand shocks Positive shocks to aggregate demand cause unemployment to fall below its natural rate, which pulls the inflation rate up. Graphing the Phillips curve =E − (u u− n)+ In the short run, policymakers face a tradeoff between and u. E + Shifting the Phillips curve The sacrifice ratio ▪ To reduce inflation, policymakers can contract agg. demand, causing unemployment to rise above the natural rate. ▪ The sacrifice ratio measures the percentage of a year’s real GDP that must be forgone to reduce inflation by 1 percentage point. ▪ A typical estimate of the ratio is 5. The sacrifice ratio ▪Example: To reduce inflation from 6 to 2 percent, must sacrifice 20 percent of one year’s GDP: GDP loss = (inflation reduction) × (sacrifice ratio) = 4 × 5 ▪ This loss could be incurred in one year or spread over several, e.g., 5% loss for each of four years. ▪ The cost of disinflation is lost GDP. One could use Okun’s law to translate this cost into unemployment. Rational expectations Ways of modeling the formation of expectations: ▪ adaptive expectations: People base their expectations of future inflation on recently observed inflation. ▪ rational expectations: People base their expectations on all available information, including information about current and prospective future policies. Painless disinflation? ▪ Proponents of rational expectations believe that the sacrifice ratio may be very small: ▪ Suppose u = un and = E = 6%, and suppose the Fed announces that it will do whatever is necessary to reduce inflation from 6 to 2 percent as soon as possible. ▪ If the announcement is credible, then E will fall, perhaps by the full 4 points. ▪ Then, can fall without an increase in u. Calculating the sacrifice ratio for the Volcker disinflation ▪1981: = 9.7% Total disinflation = 6.7% 1985: = 3.0% year u u n u−u n 1982 9.5% 6.0% 3.5% 1983 9.5 6.0 3.5 1984 7.4 6.0 1.4 1985 7.1 6.0 1.1 Total 9.5% Calculating the sacrifice ratio for the Volcker disinflation ▪ From previous slide: Inflation fell by 6.7%, total cyclical unemployment was 9.5%. ▪ Okun’s law: 1% of unemployment = 2% of lost output. ▪ Thus, 9.5% cyclical unemployment = 19.0% of a year’s real GDP. ▪ Sacrifice ratio = (lost GDP)/(total disinflation) = 19/6.7 = 2.8 percentage points of GDP were lost for each 1 percentage point reduction in inflation. The natural-rate hypothesis Our analysis of the costs of disinflation, and of economic fluctuations in the preceding chapters, is based on the natural-rate hypothesis: Changes in aggregate demand affect output and employment only in the short run. In the long run, the economy returns to the levels of output, employment, and unemployment described by the classical model (Chaps. 3–9). An alternative hypothesis: Hysteresis ▪ Hysteresis: the long-lasting influence of history on variables such as the natural rate of unemployment. ▪ Negative shocks may increase un, so economy may not fully recover. Hysteresis: Why negative shocks may increase the natural rate ▪ The skills of cyclically unemployed workers may deteriorate while unemployed, and they may not find a job when the recession ends. ▪ Cyclically unemployed workers may lose their influence on wage setting; then, insiders (employed workers) may bargain for higher wages for themselves. Result: The cyclically unemployed “outsiders” may become structurally unemployed when the recession ends. 1. Two models of aggregate supply in the short run: ▪sticky-price model ▪imperfect-information model Both models imply that output rises above its natural rate when the price level rises above the expected price level. 2. Phillips curve ▪derived from the SRAS curve ▪states that inflation depends on ▪expected inflation ▪cyclical unemployment ▪supply shocks ▪presents policymakers with a short-run tradeoff between inflation and unemployment 3. How people form expectations of inflation ▪adaptive expectations ▪ based on recently observed inflation ▪ implies “inertia” ▪ rational expectations ▪ based on all available information ▪ implies that disinflation may be painless 4. The natural rate hypothesis and hysteresis ▪the natural rate hypotheses ▪states that changes in aggregate demand can affect output and employment only in the short run ▪hysteresis ▪states that aggregate demand can have permanent effects on output and employment Solution Manual for Macroeconomics Gregory N. Mankiw 9781464182891, 9781319106058
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